About a year or two ago, I got the idea of asking the question, given the fundamental limits on how the world is put together — (1) the speed of light, which limits how fast information can get from one place to another, (2) Planck's constant, which tells you what the quantum scale is, how small things can actually get before they disappear altogether, and finally (3) the last fundamental constant of nature, which is the gravitational constant, which essentially tells you how large things can get before they collapse on themselves — how much information can possibly be processed. It turned out that the difficult part of this question was thinking it up in the first place. Once I'd managed to pose the question, it only took me six months to a year to figure out how to answer it, because the basic physics involved was pretty straightforward. It involved quantum mechanics, gravitation, perhaps a bit of quantum gravity thrown in, but not enough to make things too difficult.

The other motivation for trying to answer this question was to analyze Moore's Law. Many of our society's prized objects are the products of this remarkable law of miniaturization — people have been getting extremely good at making the components of systems extremely small. This is what's behind the incredible increase in the power of computers, what's behind the amazing increase in information technology and communications, such as the Internet, and it's what's behind pretty much every advance in technology you can possibly think of — including fields like material science. I like to think of this as the most colossal land grab that's ever been done in the history of mankind.

From an engineering perspective, there are two ways to make something bigger: One is to make it physically bigger, (and human beings spent a lot of time making things physically bigger, working out ways to deliver more power to systems, working out ways to actually build bigger buildings, working out ways to expand territory, working out ways to invade other cultures and take over their territory, etc.) But there's another way to make things bigger, and that's to make things smaller. Because the real size of a system is not how big it actually is, the real size is the ratio between the biggest part of a system and the smallest part of a system. Or really the smallest part of a system that you can actually put to use in doing things. For instance, the reason that computers are so much more powerful today than they were ten years ago is that every year and a half or so, the basic components of computers, the basic wires, logic chips etc., have gone down in size by a factor of two. This is known as Moore's Law, which is just a historical fact about history of technology.

Every time something's size goes down by a factor of two, you can cram twice as many of them into a box, and so every two years or so, the power of computers doubles, and over the course of fifty years the power of computers has gone up by a factor of a million or more. The world has gotten a million times bigger because we've been able to make the smallest parts of the world a million times smaller. This makes this an exciting time to live in, but a reasonable question to ask is, where is all this going to end? Since Moore proposed it in the early 1960s, Moore's Law has been written off numerous times. It was written off in the early 1970s because people thought that fabrication techniques for integrated circuits were going to break down and you wouldn't be able to get things smaller than a scale size of ten microns.

Now Moore's Law is being written off again because people say that the insulating barriers between wires in computers are getting to be only a few atoms thick, and when you have an insulator that's only a few atoms thick then electrons can tunnel through them and it's not a very good insulator. Well, perhaps that will stop Moore's Law, but so far nothing has stopped it.

At some point Moore's Law has to stop? This question involves the ultimate physical limits to computation: you can't send signals faster than the speed of light, you can't make things smaller than the laws of quantum mechanics tell you that you can, and if you make things too big, then they just collapse into one giant black hole. As far as we know, it's impossible to fool Mother Nature.

I thought it would be interesting to see what the basic laws of physics said about how fast, how small, and how powerful, computers can get. Actually these two questions: given the laws of physics, how powerful can computers be; and where must Moore's Law eventually stop — turn out to be exactly the same, because they stop at the same place, which is where every available physical resource is used to perform computation. So every little subatomic particle, every ounce of energy, every photon in your system — everything is being devoted towards performing a computation. The question is, how much computation is that? So in order to investigate this, I thought that a reasonable form of comparison would be to look at what I call the ultimate laptop. Let's ask just how powerful this computer could be.

The idea here is that we can actually relate the laws of physics and the fundamental limits of computation to something that we are familiar with — something of human scale that has a mass of about a kilogram, like a nice laptop computer, and has about a liter in volume, because kilograms and liters are pretty good to hold in your lap, are a reasonable size to look at, and you can put it in your briefcase, et cetera. After working on this for nearly a year what I was able to show was that the laws of physics give absolute answers to how much information you could process with a kilogram of matter confined to a volume of one liter. Not only that, surprisingly, or perhaps not so surprisingly, the amount of information that can be processed, the number of bits that you could register in the computer, and the number of operations per second that you could perform on these bits are related to basic physical quantities, and to the aforementioned constants of nature, the speed of light, Planck's constant, and the gravitational constant. In particular you can show without much trouble that the number of ops per second — the number of basic logical operations per second that you can perform using a certain amount of matter is proportional to the energy of this matter.

For those readers who are technically-minded, it's not very difficult to whip out the famous formula E = MC2 and show, using work of Norm Margolus and Lev Levitin here in Boston that the total number of elementary logical operations that you can perform per second using a kilogram of matter is the amount of energy, MC2, times two, divided by H-bar Planck's constant, times pi. Well, you don't have to be Einstein to do the calculation; the mass is one kilogram, the speed of light is 3 times ten to the eighth meters per second, so MC2 is about ten to the 17th joules, quite a lot of energy (I believe it's roughly the amount of energy used by all the world's nuclear power plants in the course of a week or so), a lot of energy, but let's suppose you could use it to do a computation. So you've got ten to the 17th joules, and H-bar, the quantum scale, is ten to the minus 34 joules per second, roughly. So there you go. I have ten to the 17th joules, I divide by ten to the minus 34 joules-seconds, and I have the number of ops: ten to the 51 ops per second. So you can perform 10 to the 51 operations per second, and ten to the 51 is about a billion billion billion billion billion billion billion ops per second — a lot faster than conventional laptops. And this is the answer. You can't do any better than that, so far as the laws of physics are concerned.